Question

What minimum distance should you separate two sources emitting the same waves with wavelength 5mm in phase such that you obtain complete destructive interference along the line connecting the sources and to the right of the sources?

Answer 1

To solve this problem we will apply the concept related to destructive interference (from the principle of superposition). This concept is understood as a superposition of two or more waves of identical or similar frequency that, when interfering, create a new wave pattern of less intensity (amplitude) at a point called a node. Mathematically it can be described as

$d = n \frac{\lambda}{2}$

Where,

d = Path difference

$\lambda$= wavelength

n = Any integer which represent the number of repetition of the spectrum

In this question the distance between the two source will be minimum for the case of minimum path difference, then n= 1

$d = \frac{\lambda}{2}$

$d = \frac{5*10^{-3}}{2}$

$d = 2.5mm$

Therefore the minimum distance that should you separate two sources emitting the same waves is 2.5mm